Fast multipole method applied to 3-D frequency domain elastodynamics

This article is concerned with the formulation and implementation of a fast multipole-accelerated BEM for 3-D elastodynamics in the frequency domain, based on the so-called diagonal form for the expansion of the elastodynamic fundamental solution, a multilevel strategy. As usual with the FM-BEM, the linear system of BEM equations is solved by GMRES, and the matrix is never explicitly formed. The truncation parameter in the multipole expansion is adjusted to the level, a feature known from recently published studies for the Maxwell equations. A preconditioning strategy based on the concept of sparse approximate inverse (SPAI) is presented and implemented. The proposed formulation is assessed on numerical examples involving O(105)O(105) BEM unknowns, which show in particular that, as expected, the proposed FM-BEM is much faster than the BEM traditional, and that the GMRES iteration count is significantly reduced when the SPAI preconditioner is used.